The twisted Grassmann graph is the block graph of a design

In this note, we show that the twisted Grassmann graph constructed by van Dam and Koolen is the block graph of the design constructed by Jungnickel and Tonchev. We also show that the full automorphism group of the design is isomorphic to the full automorphism group of the twisted Grassmann graph.Comment: 5 pages. A section on the automorphism group has been adde

Fluctuations of statistics among subregions of a turbulence velocity field

To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean energy at each scale. Their values significantly fluctuate, in lognormal distributions at least as a good approximation. Each segment is not under equilibrium between the mean rate of energy dissipation and the mean rate of energy transfer that determines the mean energy. These two rates still correlate among segments when their length exceeds the correlation length. Also between the mean rate of energy dissipation and the mean total energy, there is a correlation characterized by the Reynolds number for the whole record, implying that the large-scale flow affects each of the segments.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/

Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18

All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3), are enumerated in two different ways: once, as class regular symmetric (6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and 245 inequivalent Hermitian self-dual codes of length 18 over GF(4).Comment: 17 pages. Minor revisio

Isoscalar monopole excitations in 16^{16}O: α\alpha-cluster states at low energy and mean-field-type states at higher energy

Isoscalar monopole strength function in $^{16}$O up to $E_{x}\simeq40$ MeV is discussed. We found that the fine structures at the low energy region up to $E_{x} \simeq 16$ MeV in the experimental monopole strength function obtained by the $^{16}$O$(\alpha,\alpha^{\prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4\alpha$ cluster model, while the gross three bump structures observed at the higher energy region ($16 \lesssim E_{x} \lesssim 40$ MeV) look likely to be approximately reconciled by the mean-field calculations such as RPA and QRPA. In this paper, it is emphasized that two different types of monopole excitations exist in $^{16}$O; one is the monopole excitation to cluster states which is dominant in the lower energy part ($E_{x} \lesssim 16$ MeV), and the other is the monopole excitation of the mean-field type such as one-particle one-hole ($1p1h$) which {is attributed} mainly to the higher energy part ($16 \lesssim E_{x} \lesssim 40$ MeV). It is found that this character of the monopole excitations originates from the fact that the ground state of $^{16}$O with the dominant doubly closed shell structure has a duality of the mean-field-type {as well as} $\alpha$-clustering {character}. This dual nature of the ground state seems to be a common feature in light nuclei.Comment: 35 pages, 5 figure

On Landau's prediction for large-scale fluctuation of turbulence energy dissipation

Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuration for turbulence production. With an increase of scale r above the scale of largest energy-containing eddies, the fluctuation becomes to have the scaling r^-1/2 and becomes close to Gaussian. We also confirm that the large-scale fluctuation affects small-scale statistics.Comment: 9 pages, accepted by Physics of Fluids (see http://pof.aip.org

Convex Functions and Spacetime Geometry

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed, references adde

Competition between Hidden Spin and Charge Orderings in Stripe Phase

The correlation between charge and spin orderings in hole-doped antiferromagnets is studied within an effective model of quantum strings fluctuating in an antiferromagnetic background. In particular, we perform the direct estimation of the charge and spin long-range-order parameters by means of the quantum Monte Carlo simulation. A hidden spin long-range order is found to be governed by a competition between the two trends caused by increasing hole mobility: the enhancement of the two-dimensional spin-spin correlation mediated by hole motions and the reformation of a strong stripe order.Comment: 4 pages, 8 figures. Accepted for publication as a Rapid Communication in Physical Review

Spectral Decomposition of Path Space in Solvable Lattice Model

We give the {\it spectral decomposition} of the path space of the U_q(\hatsl) vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the \hatsl level $l$ integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the \hatsl level $l$ integrable representations in consequence.Comment: 27 pages, Plain Tex, epsf.tex, 7 figures; minor revision. identical with the version to be published in Commun.Math.Phy

Dynamics of a string coupled to gravitational waves - Gravitational wave scattering by a Nambu-Goto straight string

We study the perturbative dynamics of an infinite gravitating Nambu-Goto string within the general-relativistic perturbation framework. We develop the gauge invariant metric perturbation on a spacetime containing a self-gravitating straight string with a finite thickness and solve the linearized Einstein equation. In the thin string case, we show that the string does not emit gravitational waves by its free oscillation in the first order with respect to its oscillation amplitude, nevertheless the string actually bends when the incidental gravitational waves go through it.Comment: Published in Physical Review D. Some explanations are changed to clarify our point